Approximately 14 percent of the population of Arizona is 65 years or older.A random sample of five persons from this population is taken.The probability that less than 2 of the 5 are 65 years or older is:
A) 0.8533
B) 0.1467
C) 0.4704
D) 0.3829
E) None of these.

Question

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula, which is P(X = k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and nCk is the binomial coefficient. Here, n=5 (five persons), p=0.14 (14 percent chance of being 65 years or older), and we're looking for the probability of having less than 2 people 65 or older, which means we need to calculate P(X<2) = P(X=0) + P(X=1). Calculating these probabilities and adding them gives us approximately 0.8533, indicating that there's about an 85.33% chance that less than 2 of the 5 people sampled will be 65 years or older.

Approximately 14 Percent of the Population of Arizona Is 65